Related papers: Quantum and semi-classical aspects of confined systems with variable mass

Quantum and semi-classical aspects of confined systems with variable mass

URL: http://arxiv.org/abs/2005.14231v1
Date: Thu, 28 May 2020 18:50:24 GMT
Title: Quantum and semi-classical aspects of confined systems with variable mass
Authors: Jean-Pierre Gazeau, V\'eronique Hussin, James Moran, and Kevin Zelaya
Abstract summary: We explore the quantization of classical models with position-dependent mass terms constrained to a bounded interval in the canonical position. For a non-separable function $Pi(q,p)$, a purely quantum minimal-coupling term arises in the form of a vector potential for both the quantum and semi-classical models.
Score: 0.3149883354098941
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We explore the quantization of classical models with position-dependent mass (PDM) terms constrained to a bounded interval in the canonical position. This is achieved through the Weyl-Heisenberg covariant integral quantization by properly choosing a regularizing function $\Pi(q,p)$ on the phase space that smooths the discontinuities present in the classical model. We thus obtain well-defined operators without requiring the construction of self-adjoint extensions. Simultaneously, the quantization mechanism leads naturally to a semi-classical system, that is, a classical-like model with a well-defined Hamiltonian structure in which the effects of the Planck's constant are not negligible. Interestingly, for a non-separable function $\Pi(q,p)$, a purely quantum minimal-coupling term arises in the form of a vector potential for both the quantum and semi-classical models.

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